Occupy Boston protesters remained firmly entrenched in a downtown city square early Friday after a midnight deadline passed for them to clear out or face eviction.

Demonstrators cleared trash and some of the more than 100 tents from the area, but most stayed put. Police presence was light around Dewey Square.

Superior Court Judge Frances A. McIntyre ruled Wednesday that demonstrators' First Amendment rights do not extend to seizing and holding areas on which they sit.

Authorities are "obligated by law to preserve Dewey Square as a space open to the public," McIntyre added.

Boston Mayor Thomas M. Menino, who in the past has appeared to tolerate his city's chapter of the nationwide movement, recently signaled that the park could be a safety hazard as winter weather rolls in.

"We're asking them to leave, according to their own will and volition," Menino told CNN affiliate WCVB. "After that, we'll make decisions about how we'll clear off the site in the future."

In October, 129 people were arrested during a demonstration in which protesters allegedly blocked traffic and refused to disperse, according to police spokesman Eddy Chrispin.

They were arrested mostly for "unlawful assembly and trespassing," he said.

The movement, which first sprang up in a Lower Manhattan park, seeks to highlight what it sees as corruption and growing income disparities between the nation's richest 1% and the rest of the country.

In a move similar to McIntyre's ruling, a New York Supreme Court announced last month that Occupy protesters would be allowed to return to Zuccotti Park -- considered a home base for demonstrators -- but would be restricted from camping overnight.

Police in riot gear cleared them out in the early-morning hours in mid-November, a move that attorneys for the demonstrators have said was unlawful.

Thousands later deluged the city's financial district in a show of strength echoed nationwide as part of the group's so-called "mass day of action."

Scores were arrested across the city, and several police officers were reported injured, as thousands of others gathered in places such as St. Louis, San Francisco, Denver and Milwaukee to respond to the "day of action" plea.

Last month, police in Los Angeles and Philadelphia dismantled tents and arrested Occupy protesters who refused to leave city areas.

In Philadelphia, police arrested 52 people after scuffles broke out when authorities ordered some protesters to clear the street.

Encampments have largely remained in a handful of cities, including San Francisco; Asheville, North Carolina; Oklahoma City; and Washington, according to media reports and group websites.